Wear amount estimation method, wear amount estimation device, and wear amount estimation program

ABSTRACT

A wear amount estimation device estimates plural kinds of wear energy depending on each of an internal pressure of aircraft tires, a load acting on the aircraft tires, a velocity of an aircraft, a slip angle caused in the aircraft tires, and a braking force of the aircraft, in accordance with each of these elements and wear energy EFR of the aircraft tires in a state of a free rolling run The wear amount estimation device estimates the wear amount wear of the aircraft tires in accordance with each of the calculated wear energy and a wear resistance R indicating a relationship between predetermined wear energy and a predetermined wear amount.

TECHNICAL FIELD

The present invention relates to a wear amount estimation method, a wearamount estimation device, and a wear amount estimation program.

BACKGROUND ART

A technique is known that estimates a wear amount of aircraft tires (forexample, Patent Literature 1). The method disclosed in Patent Literature1 acquires plural kinds of wear energy corresponding to plural runningstates (such as a touching down state, a deceleration state aftertouching down, and a taxiing state) classified depending on theconditions of use, and estimates the wear amount of the respectiveaircraft tires based on the acquired wear energy. The method disclosedin Patent Literature 1 uses measurement data of a test device disclosedin Patent Literature 2, for example, when estimating the wear amount ofthe aircraft tires.

CITATION LIST Patent Literature

Patent Literature 1: Japanese Unexamined Patent Application PublicationNo. 2013-113724

Patent Literature 2: Japanese Patent No. 4198610

SUMMARY OF INVENTION

The method disclosed in Patent Literature 1 still may not be able toaccurately estimate the wear amount of the respective aircraft tires inthe situation in which the aircraft tires are actually used. The reasonfor this is that, in the situation in which the aircraft tires areactually used, the wear amount of the aircraft tires typically greatlyvaries depending on the state of the ground surface in each airport, adistance necessary for taxiing, a frequency of circling, a total weightof an aircraft body, and the position of the center of gravity of theaircraft body which changes due to seating positions of passengers orbaggage, for example. The method disclosed in Patent Literature 1 thuscannot accurately estimate the wear amount of the respective aircrafttires in the situation in which the aircraft tires are actually used ifthe measurement data does not include these pieces of information.

To solve the conventional problem described above, the present inventionprovides a wear amount estimation method, a wear amount estimationdevice, and a wear amount estimation program capable of accuratelyestimating a wear amount of aircraft tires in a situation in which theaircraft tires are actually used.

Technical Solution

A wear amount estimation method according to the present inventioncalculates wear energy E_(P), which depends on an internal pressure ofthe aircraft tires, in accordance with the internal pressure and wearenergy E_(FR) of the aircraft tires in a state of a free rolling run.The wear amount estimation method calculates wear energy E_(L), whichdepends on a load acting on the aircraft tires, in accordance with theload and the wear energy E_(FR). The wear amount estimation methodcalculates wear energy E_(V), which depends on a velocity of theaircraft, in accordance with the velocity and the wear energy E_(FR).The wear amount estimation method calculates wear energy ΔE_(S), whichdepends on a slip angle caused in the aircraft tires, in accordance withthe slip angle and the wear energy E_(FR). The wear amount estimationmethod calculates wear energy ΔE_(B), which depends on a braking forceof the aircraft, in accordance with the braking force and the wearenergy E_(FR). The wear amount estimation method estimates the wearamount wear of the aircraft tires in accordance with the wear energyE_(P), the wear energy E_(L), the wear energy E_(V), the wear energyΔE_(S), the wear energy ΔE_(B), and a wear resistance R indicating arelationship between predetermined wear energy and a predetermined wearamount.

Advantageous Effects

The present invention can accurately estimate the wear amount of theaircraft tires in a situation in which the aircraft tires are actuallyused.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A is a schematic view showing a relation between a wear amountestimation device, a network, and an airline.

FIG. 1B is a schematic configuration diagram of the wear amountestimation device according to the present embodiment of the presentinvention.

FIG. 2 is a flowchart for illustrating an operation of the wear amountestimation device according to the present embodiment of the presentinvention.

FIG. 3 is a graph showing a relationship between braking G and a brakepressure.

FIG. 4 is a graph showing a relationship between an internal pressure ofan aircraft tire and wear energy.

FIG. 5 is a graph showing a relationship between a load acting on theaircraft tire and the wear energy.

FIG. 6 is a graph showing a relationship between a velocity of theaircraft and the wear energy.

FIG. 7 is a graph showing a relationship between a slip angle caused inthe aircraft tire and the wear energy.

FIG. 8 is a graph showing a relationship between a braking force of theaircraft and the wear energy.

FIG. 9 is a back view illustrating circumferential grooves and ribsprovided on the aircraft tires.

FIG. 10 is a flowchart for illustrating an operation of the wear amountestimation device according to the present embodiment of the presentinvention.

FIG. 11 is a side view for illustrating a static load of the aircraft.

FIG. 12 is a side view for illustrating a dynamic load of the aircraft.

FIG. 13 is a back view for illustrating the dynamic load of theaircraft.

DESCRIPTION OF EMBODIMENTS

Hereinafter, an embodiment according to the present invention will bedescribed with reference to the drawings. The same elements illustratedin the drawings are indicated by the same reference numerals, andoverlapping explanations are not made below.

As illustrated in FIG. 1A, a wear amount estimation device 10 is ageneral-purpose computer, for example, including a processor including aCPU and a memory such as a read-only memory (ROM) and a random-accessmemory (RAM). The CPU reads out a program stored in the ROM to the RAMand executes the program. The wear amount estimation device 10 may beeither a built-in terminal device or a mobile terminal device easy tocarry (such as a smartphone). The wear amount estimation device 10includes a communication unit 11, a calculation unit 12, and anestimation unit 13, as illustrated in FIG. 1B. The communication unit 11is an interface connected to a network 20 to transfer/receive pieces ofdata to communicate with an airline 30. The calculation unit 12calculates wear energy. The estimation unit 13 estimates the wear amountof aircraft tires. The communication unit 11, the calculation unit 12,and the estimation unit 13 can be fabricated in single or pluralprocessing circuits. The respective processing circuits include aprogrammed processing device, such as a processing device including anelectric circuit. The respective processing circuits include anapplication-specific integrated circuit (ASIC) configured to execute thefunctions described above or a device including circuit components.

The wear amount estimation device 10 mutually communicates with theairline 30 via the network 20. The wear amount estimation device 10acquires pieces of information from the airline 30 via the network 20 toestimate the wear amount of the aircraft tires mounted on an aircraft.The information that the wear amount estimation device 10 acquires fromthe airline 30 will be described below. As used herein, the aircraft maybe simply referred to as a “body”. The network 20 is a communicationsnetwork capable of communicating various kinds of information. Forexample, the network is implemented by various types of communicationlines, such as dedicated lines installed by telecommunications carriers,public switched telephone networks, satellite communication lines, andmobile communication lines.

An example of operation of the wear amount estimation device 10 isdescribed below with reference to FIG. 2.

In step S101, the wear amount estimation device 10 acquires wear energyE_(FR) of the aircraft tires during taxiing.

The term “taxiing” refers to a state in which the aircraft runs on theground (mainly a runway) under the power of the aircraft. The state oftaxiing includes a state of a free rolling run, a state of adecelerating run, and a state of a circling run. The state of the freerolling run refers to a state in which the aircraft runs straight byrolling without braking force acting on the aircraft tires. The state ofthe decelerating run refers to a running state when the braking force isapplied to the aircraft tires. The state of the circling run refers to arunning state when a slip angle is applied to the aircraft tires.

The wear energy E_(FR) is energy per unit area produced at a particularpoint on the surface of the corresponding aircraft tire when theaircraft tire passes through a road surface once, and its unit is J/m².The wear energy E_(FR) is particularly wear energy during the state ofthe free rolling run. The wear amount estimation device 10 may acquirethe wear energy E_(FR) through laboratory testing, or may acquire thewear energy E_(FR) by a finite element method (FEM).

The process proceeds to step S102, and the wear amount estimation device10 acquires information on braking G acting on the body of the aircraft.In particular, the wear amount estimation device 10 acquires informationabout the braking G acting on the body and a brake signal. The brakesignal refers to a brake pressure regarding a hydraulic brake. Thebraking force of the body is not achieved only with the aircraft tires,which is different from typical automobiles. The braking G of the bodydoes not correspond to the braking G acting on the aircraft tires. Thewear amount estimation device 10 thus obtains the braking G applied tothe aircraft tires so as to estimate the wear amount of the aircrafttires. As shown in FIG. 3, a predetermined value A is a point at whichthe braking force of a brake and a propulsive force of an engine arebalanced, while the braking G is not led to any negative number when thebrake pressure is the predetermined value A or smaller. The braking Gdoes not change when the brake pressure of a predetermined value 13 orgreater is applied. This braking force of the brake is given by thefollowing function represented by the formula A1:

[Math. 1]

G _(x) ^(BR)=min(0,max(G _(max) ^(BR) ,f(BP)))  (A1)

where BP is the brake pressure, and G_(MAX) ^(BR) is the maximum brakingG of the brake. G_(MAX) ^(BR) is normally a negative number.

The braking force of the brake is given by the following functionrepresented by the formula A2 when subjected to a linear approximationas shown in FIG. 3:

[Math. 2]

G _(x) ^(BR)=min(0,max(G _(max) ^(BR) ,a×BP+b))  (A2)

where a and b are constants assigned to each body.

The wear amount estimation device 10 can calculate the braking G actingon the aircraft tires according to the above formula A2 at apredetermined timing. While the above process has been illustrated withthe hydraulic brake, the aircraft is not limited to the hydraulic braketo be equipped. The aircraft may be equipped with an electric brake. Thewear amount estimation device 10 can also calculate the braking G whenthe aircraft tire is equipped with an electric brake in the same manneras described above.

The wear amount estimation device 10 according to the present embodimentchanges the internal pressure of the aircraft tires on the basis of thewear energy E_(FR) during the state of the free rolling run, andacquires wear energy E_(P) which depends on the internal pressure. Asshown in FIG. 4, the wear energy E_(P) is represented by a quadraticfunction. A relationship between ribs formed on the aircraft tires andthe wear energy E_(FR) is described below with reference to FIG. 9.While the following explanation is made with regard to the aircrafttires for a main gear illustrated in FIG. 9, the same is also applied tothe aircraft tires for a nose gear.

As illustrated in FIG. 9, the respective aircraft tires 40 to 43 areprovided with a plurality of circumferential grooves 60 (three in FIG.9) extending in the tire circumferential direction on the tread track,and are provided with a plurality of ribs (four in FIGS. 9) 50 to 53defined by the respective circumferential grooves 60. The ribs 50, 51,52, and 53 are arranged in this order from the central side to the outerside of the body. The wear energy E_(FR) varies depending on thepositions of the ribs. The wear amount estimation device 10 thenacquires the wear energy E_(FR) of the respective ribs 50 to 53 of oneaircraft tire. The wear amount estimation device 10 may acquire, as thewear energy E_(FR), an average value of the wear energy E_(FR) regardingthe rib 50 closest to the central side and the wear energy E_(FR)regarding the rib 53 on the outermost side.

The wear energy E_(P), which depends on the internal pressure of theaircraft tires, also varies depending on the positions of the ribs shownin FIG. 9. When the positions of the ribs of the aircraft tires arerepresented by use of a variable i in the state in which the aircrafttires are mounted on the aircraft, the wear energy E_(P) is given by thefollowing formula A3:

[Math. 3]

E _(P) ^(i)(P)=a _(P) P ² +b _(P) P+c _(P)  (A3)

where i is the position of each rib of the aircraft tire, P is theinternal pressure of the aircraft tire, and a_(P), b_(P), and c_(P) areconstants.

The wear amount estimation device 10 also changes the load applied tothe aircraft tires on the basis of the wear energy E_(FR) during thestate of the free rolling run, and acquires wear energy E_(L) whichdepends on the load. As shown in FIG. 5, the wear energy E_(L) isrepresented by a quadratic function. The wear energy E_(L) also variesdepending on the positions of the ribs shown in FIG. 9, as in the caseof the wear energy E_(P). When the positions of the ribs of the aircrafttires are represented by use of the variable i in the state in which theaircraft tires are mounted on the aircraft, the wear energy E_(L) isgiven by the following formula A4:

[Math. 4]

E _(L) ^(i)(L)=a _(L) L ² +b _(L) L+c _(L)  (A4)

where i is the position of each rib of the aircraft tire, L is the loadapplied to the aircraft tire, and a_(L), b_(L), and c_(L) are constants.

The wear amount estimation device 10 also changes the velocity of theaircraft on the basis of the wear energy E_(FR) during the state of thefree rolling run, and acquires wear energy E_(V) which depends on thevelocity. As shown in FIG. 6, the wear energy E_(V) is represented by aquadratic function. The wear energy E_(V) also varies depending on thepositions of the ribs shown in FIG. 9, as in the case of the wear energyE_(P). When the positions of the ribs of the aircraft tires arerepresented by use of the variable i in the state in which the aircrafttires are mounted on the aircraft, the wear energy E_(L) is given by thefollowing formula A5:

[Math. 5]

E _(V) ^(i)(V)=a _(V) V ² +b _(V) V+c _(V)  (A5)

where i is the position of each rib of the aircraft tire, V is thevelocity of the aircraft, and a_(V), b_(V), and c_(V) are constants.

The wear amount estimation device 10 also changes the slip angle (SA) ofthe aircraft tires, and acquires wear energy E_(S) depending on the SAas a difference from the wear energy E_(FR) in the state of the freerolling run. As shown in FIG. 7, the wear energy E_(S) is represented bya quadratic function. The wear energy E_(S) also varies depending on thepositions of the ribs shown in FIG. 9, as in the case of the wear energyE_(P). When the positions of the ribs of the aircraft tires arerepresented by use of the variable i in the state in which the aircrafttires are mounted on the aircraft, the wear energy E_(S) is given by thefollowing formula A6:

[Math. 6]

ΔE _(S) ^(i)(SA)=a _(S)(SA)² +b _(S)(SA)+c _(S) −E _(FR)  (A6)

where i is the position of each rib of the aircraft tire, SA is the slipangle, and a_(S), b_(S), and c_(S) are constants.

The wear amount estimation device 10 also changes the braking force ofthe aircraft, and acquires wear energy E_(B) depending on the breakingforce as a difference from the wear energy E_(FR) in the state of thefree rolling run. As shown in FIG. 8, the wear energy E_(B) isrepresented by a quadratic function. The wear energy E_(B) also variesdepending on the positions of the ribs shown in FIG. 9, as in the caseof the wear energy E_(P). When the positions of the ribs of the aircrafttires are represented by use of the variable i in the state in which theaircraft tires are mounted on the aircraft, the wear energy E_(B) isgiven by the following formula A7:

[Math. 7]

ΔE _(B) ^(i)(G _(x) ^(BR))=a _(B)(G _(x) ^(BR))² +b _(B)(G _(x) ^(BR))+c_(B) −E _(FR)  (A7)

where i is the position of each rib of the aircraft tire, G_(X) ^(BR) isthe braking force of the aircraft, and a_(B), b_(B), and c_(B) areconstants.

Next, an example of an estimating process of the wear amount estimationdevice 10 is described below with reference to FIG. 10. The estimatingprocess of the wear amount estimation device 10 includes six steps (stepS201 to step S206).

In step S201, the wear amount estimation device 10 acquires pieces ofinformation on the aircraft from the airline 30. In particular, the wearamount estimation device 10 acquires the velocity of the aircraft, theacceleration of the aircraft, the current position of the aircraft, thedirection of the nose of the aircraft, the total weight of the aircraft,the internal pressure and the positions of the ribs of the respectiveaircraft tires mounted on the aircraft, the brake pressure of theaircraft, the circling angle of the body, the circling radius of thebody, and the steering angle of the steering wheel, for example. Thewear amount estimation device 10 also acquires the time when therespective pieces of the information are acquired.

The process proceeds to step S202, and the wear amount estimation device10 calculates a wheel load (a load) of the aircraft tires. The wheelload of the aircraft tires is obtained from a static load and a dynamicload.

The wear amount estimation device 10 first calculates the position ofthe center of gravity of the body when calculating the wheel load of theaircraft tires. The position of the center of gravity of the body variesdepending on the seating positions of passengers or baggage. In thetechnical field of aircrafts, a method is known that confirms the weightand the position of the center of gravity in accordance with theprovisions of the law (the aviation law). The position of the center ofgravity during flight can be measured relative to a mean aerodynamicchord (MAC), so as to calculate the position of the center of gravity inassociation with the positional information of the MAC. For example,when the position of the center of gravity is calculated with acoordinate system based on the nose gear, the position of the center ofgravity of the body can be calculated according to the mathematicalexpression of L1+L2×% MAC, where L1 is a distance from the nose gear tothe front edge of the MAC position, and L2 is a MAC length of the body.L1 and L2 can be typically obtained from the body specifications. Inaddition, % MAC is available as the information prescribed in theaviation law.

The static load of the aircraft tires is described below with referenceto FIG. 11. When the influence of the velocity of the aircraft is small,such as the state of taxiing, namely, when the influence of a liftingforce can be ignored, the static load is calculated in accordance with abalance of a moment about the center of gravity acting on the body. Asillustrated in FIG. 11, the total weight W_(N) of the nose gear isrepresented by the following formula A8:

[Math.  8] $\begin{matrix}{W_{N} = {W \times \frac{D\; 3}{D\; 4}}} & ({A8})\end{matrix}$

where W is the total weight of the body, D3 is a distance from theposition of the center of gravity to the main gear, and D4 is a distancefrom the nose gear to the main gear.

Similarly, as illustrated in FIG. 11, the total weight W_(M) of the maingear is represented by the following formula A9:

[Math.  9] $\begin{matrix}{W_{M} = {W \times \frac{D\; 2}{D\; 4}}} & ({A9})\end{matrix}$

where D2 is a distance from the nose gear to the position of the centerof gravity.

When the load applied to the aircraft tires is presumed to bedistributed evenly, the wheel load of the respective aircraft tiresmounted on the nose gear is obtained by dividing the total weight W_(N)by the number of the tires mounted on the nose gear. In addition, thewheel load of the respective aircraft tires mounted on the main gear isobtained by dividing the total weight W_(M) by the number of the tiresmounted on the main gear. When there is measurement data on the wheelload, the distribution is preferably made according to the data.

The lifting force G_(lift) is generated depending on the velocity whenthe aircraft takes off, which is represented by the following formulaA10:

[Math. 10]

G _(lift) =cV ²  (A10)

where c is a constant, and v is the velocity of the aircraft.

The acceleration in the vertical direction measured in the body of theaircraft when taking off gradually decreases as the aircraftaccelerates. As in the case of the braking G described in step S102shown in FIG. 2, a relationship between the acceleration of the body inthe vertical direction and the square of the velocity is preliminarilyobtained, so as to calculate the total weight W that the aircraft tiresbear during takeoff. The total weight W that the aircraft tires bearduring takeoff is represented by the following formula A11:

[Math. 11]

W=M(1−G _(lift))  (A11)

where M is the total weight of the body, which is the same value as W inthe unit system of kg and kgf.

The dynamic load of the aircraft tires is described below with referenceto FIG. 12 and FIG. 13. A load shift due to the acceleration in thefront-rear direction acting on the center of gravity of the body isfirst described below with reference to FIG. 12.

As illustrated in FIG. 12, when a load change of the respective aircrafttires is represented by ΔF_(Z) ^(j) (j: the mounted position of eachaircraft tire), the following formula A12 and formula A13 need to befulfilled in view of the balance of the acceleration in the front-reardirection of the body with the moment, and the total weight of the bodywhich is constant:

[Math. 12]

z _(g) F _(x)=Σ_(j=1) ^(N) ΔF _(z) ^(j) x ^(j)  (A12)

[Math. 13]

Σ_(j=1) ^(N) ΔF _(z) ^(j)=0  (A13)

where j is the mounted position of each aircraft tire, N is the totalnumber of the aircraft tries mounted on the main gear, Zg is thedistance from the ground to the position of the center of gravity, andFx is the moment due to the acceleration in the front-rear direction ofthe body.

When the load shift is presumed to be proportional to the position inthe front-rear direction, the load change ΔF_(z) ^(j) is represented bythe following formula A14:

[Math. 14]

ΔF _(z) ^(i)=α_(x) x _(j)+β_(x)  (A14)

Since the total weight of the aircraft is constant, the followingformula A15 and formula A16 are fulfilled:

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 15} \right\rbrack & \; \\{{\sum\limits_{j = 1}^{N}\; {\Delta \; F_{z}^{j}}} = {{{\alpha_{x}{\sum\limits_{j = 1}^{N}\; x^{j}}} + {N\; \beta_{x}}} = 0}} & \left( {A\; 15} \right) \\\left\lbrack {{Math}.\mspace{14mu} 16} \right\rbrack & \; \\{\beta_{x} = {- \frac{\alpha_{x}{\sum\limits_{j = 1}^{N}\; x^{j}}}{N}}} & \left( {A\; 16} \right)\end{matrix}$

The following formula A17 and formula A18 are fulfilled due to thebalance of the moment:

$\begin{matrix}{\mspace{76mu} \left\lbrack {{Math}.\mspace{14mu} 17} \right\rbrack} & \; \\{{z_{g}F_{x}} = {{\sum\limits_{j = 1}^{N}\; {\Delta \; F_{z}^{j}x^{j}}} = {{{\alpha_{x}{\sum\limits_{j = 1}^{N}\; \left( x^{j} \right)^{2}}} - {\frac{\alpha_{x}}{N}\left( {\sum\limits_{j = 1}^{N}\; x^{j}} \right)^{2}}} = {\alpha_{x}\left\{ {{\sum\limits_{j = 1}^{N}\; \left( x^{j} \right)^{2}} - {\frac{1}{N}\left( {\sum\limits_{j = 1}^{N}\; x^{j}} \right)^{2}}} \right\}}}}} & \left( {A\; 17} \right) \\{\mspace{76mu} \left\lbrack {{Math}.\mspace{14mu} 18} \right\rbrack} & \; \\{\mspace{76mu} {\alpha_{x} = \frac{z_{g}F_{x}}{\left\{ {{\sum\limits_{j = 1}^{N}\; \left( x^{j} \right)^{2}} - {\frac{1}{N}\left( {\sum\limits_{j = 1}^{N}\; x^{j}} \right)^{2}}} \right\}}}} & \left( {A\; 18} \right)\end{matrix}$

As described above, the wear amount estimation device 10 can calculatethe load variation at the position of the corresponding aircraft tirecaused by the acceleration in the front-rear direction of the body.

A load shift due to the acceleration in the right-left direction (thelateral direction) acting on the center of gravity of the body is thendescribed below with reference to FIG. 13.

As illustrated in FIG. 13, when the load change of the respectiveaircraft tires is represented by ΔF_(Z) ^(j) (j: the mounted position ofeach aircraft tire), the following formula A19 and formula A20 need tobe fulfilled in view of the balance of the acceleration in theright-left direction of the body with the moment, and the total weightof the body which is constant:

[Math. 19]

z _(g) F _(y)=Σ_(j=1) ^(N) ΔF _(z) ^(j) y ^(j)  (A19)

[Math. 20]

Σ_(j=1) ^(N) ΔF _(z) ^(j)=0  (A20)

where j is the mounted position of each aircraft tire, N is the totalnumber of the aircraft tries mounted on the main gear, Zg is thedistance from the ground to the position of the center of gravity, andFy is the moment due to the acceleration in the right-left direction ofthe body.

When the load shift is presumed to be proportional to the position inthe right-left direction, the condition in which the total weight of thebody is constant is fulfilled as long as the aircraft tires aresymmetrically mounted, so as to fulfill the following formula A21:

[Math. 21]

ΔF _(z) ^(j)=α_(y) y _(j)  (A21)

The following formula A22 is fulfilled due to the balance of the moment:

[Math.  22] $\begin{matrix}{\alpha_{y} = \frac{z_{g}F_{y}}{\sum\limits_{j = 1}^{N}\; y_{j}^{2}}} & ({A22})\end{matrix}$

As described above, the wear amount estimation device 10 can calculatethe load variation at the position of the corresponding aircraft tirecaused by the acceleration in the right-left direction of the body.

The dynamic load (the change) caused due to the acceleration of the bodyis represented by the following formula A23 when using the load shift asdescribed with reference to FIG. 12 and FIG. 13:

     [Math.  23] $\begin{matrix}{{\Delta \; F_{z}^{j}} = {{{\alpha_{x}x_{j}} + \beta_{x} + {\alpha_{y}y_{j}}} = {{\frac{z_{g}F_{x}}{\left\{ {{\sum\limits_{j = 1}^{N}\; \left( x^{j} \right)^{2}} - {\frac{1}{N}\left( {\sum\limits_{j = 1}^{N}\; x^{j}} \right)^{2}}} \right\}} \cdot \left( {x_{j} - \frac{\sum\limits_{j = 1}^{N}\; x^{j}}{N}} \right)} + {\frac{z_{g}F_{y}}{\sum\limits_{j = 1}^{N}\; y_{j}^{2}} \cdot y_{j}}}}} & ({A23})\end{matrix}$

For example, the wheel load acting on the respective aircraft tires ofthe main gear is represented by the following formula A24:

     [Math.  24] $\begin{matrix}{W^{j} = {{W_{M}^{s} + {\Delta \; F_{z}^{j}}} = {W_{M}^{s} + {\frac{z_{g}F_{x}}{\left\{ {{\sum\limits_{j = 1}^{N}\; \left( x^{j} \right)^{2}} - {\frac{1}{N}\left( {\sum\limits_{j = 1}^{N}\; x^{j}} \right)^{2}}} \right\}} \cdot \left( {x_{j} - \frac{\sum\limits_{j = 1}^{N}\; x^{j}}{N}} \right)} + {\frac{z_{g}F_{y}}{\sum\limits_{j = 1}^{N}\; y_{j}^{2}} \cdot y_{j}}}}} & ({A24})\end{matrix}$

where W_(M) ^(S) is the wheel load with no acceleration in thefront-rear direction or no acceleration in the right-left direction.

W_(M) ^(S) is given by the following formula A25:

[Math.  25] $\begin{matrix}{W_{M}^{s} = \frac{W_{M}}{N}} & ({A25})\end{matrix}$

where N is the total number of the aircraft tires mounted on the maingear. As described above, the wheel load differs between the state oftaxiing and the state of takeoff.

The process proceeds to step S203 shown in FIG. 10, and the wear amountestimation device 10 acquires the brake pressure of the aircraft tocalculate the braking force. The method of calculating the braking forcecan be the same as described in step S102 shown in FIG. 2.

The process proceeds to step S204, and the wear amount estimation device10 acquires the circling angle and the circling radius of the body, andthe steering angle of the steering wheel so as to calculate the SA ofthe aircraft tires. The method of calculating the SA of the aircrafttires can be the same as a calculation method for a SA of automobiletires, and the specific explanations are not made below.

The process proceeds to step S205, and the wear amount estimation device10 calculates instant wear energy dE_(w). The instant wear energy dE_(w)refers to wear energy generated during a quite short period of time dt,and is represented by the following formula A26 by use of the aboveformulas A3 to A7:

     [Math.  26] $\begin{matrix}{{dE}_{w}^{i} = {{E_{P}^{i}(P)} \cdot {E_{L}^{i}(L)} \cdot {E_{V}^{i}(V)} \cdot \left\{ {E_{FR}^{i} + {\Delta \; {E_{S}^{i}(S)}} + {\Delta \; {E_{B}^{i}(B)}}} \right\} \cdot \frac{Vdt}{2\pi \; r}}} & ({A26})\end{matrix}$

where r is the circling radius of the body.

The wear energy E_(w) generated during taxiing is obtained byintegrating the formula A26 with the time T (a predetermined time)during which the aircraft is taxiing, and is represented by thefollowing formula A27:

[Math. 27]

E _(w) ^(i)=∫₀ ^(T) dE _(w) ^(i)  (A27)

The formula A27 can be approximated by the following formula A28 whenthe sampling period is represented by ΔT:

     [Math.  28] $\begin{matrix}{E_{w}^{i} = {{\int_{0}^{T}{dE}_{w}^{i}} \approx {\Sigma \; {{E_{P}^{i}(P)} \cdot {E_{L}^{i}(L)} \cdot {E_{V}^{i}(V)} \cdot \left\{ {E_{FR}^{i} + {\Delta \; {E_{S}^{i}(S)}} + {\Delta \; {E_{B}^{i}(B)}}} \right\} \cdot \frac{V\; \Delta \; t}{2\pi \; r}}}}} & ({A28})\end{matrix}$

The process proceeds to step S206, and the wear amount estimation device10 calculates an instant wear amount dwear^(i) of the aircraft tiresbased on the calculated instant wear energy dE_(w). For example, thewear amount estimation device 10 can calculate the instant wear amountof the aircraft tires by use of the instant wear energy dE_(w) and awear resistance R. The wear resistance R is represented by the followingformula A29 by use of wear energy E′ per flight and the wear amount w′per flight calculated from the behavior of the body during an averageflight (between an airport and an airport), for example. Namely, thewear resistance R indicates the relationship between predetermined wearenergy and a predetermined wear amount.

[Math.  29] $\begin{matrix}{E = \frac{E^{\prime}}{w^{\prime}}} & ({A29})\end{matrix}$

The instant wear amount dwear^(i) of the aircraft tires is representedby the following formula A30:

[Math.  30] $\begin{matrix}{{dwear}^{i} = \frac{{dE}_{w}^{i}}{R}} & ({A30})\end{matrix}$

The wear amount estimation device 10 repeatedly executes the processfrom step S202 to step S206 per quite short period of time dt, so as tocalculate the wear amount wear^(i) of the aircraft tires. The wearamount wear^(i) of the aircraft tires during the time T in which theaircraft is taxiing is represented by the following formula A31:

[Math.  31] $\begin{matrix}{{wear}^{i} = \frac{E_{w}^{i}}{R}} & ({A31})\end{matrix}$

(Operational Effects)

As described above, the wear amount estimation device 10 estimates thewear amount of the aircraft tires mounted on the aircraft in accordancewith the internal pressure of the aircraft tires actually used, the loadacting on the aircraft tires, the velocity of the aircraft, the slipangle caused in the aircraft tires, and the braking force of theaircraft tires. The wear amount estimation device 10 thus can estimatethe wear amount of the aircraft tires with a high accuracy in thesituation in which the aircraft tires are actually used. The informationacquired from the airline 30 is information without RF tags attached tothe aircraft tires. The wear amount estimation device 10 thus canaccurately estimate the wear amount of the aircraft tires without RFtags attached to the aircraft tires.

The wear amount estimation device 10 calculates the wear energy E_(p),the wear energy E_(L), the wear energy E_(V), the wear energy ΔE_(S),and the wear energy ΔE_(B) in accordance with the positions of the ribsof the aircraft tires in the state in which the aircraft tires aremounted on the aircraft. Each of the wear energy varies depending on thepositions of the ribs. The wear amount estimation device 10 according tothe present embodiment calculates each of the wear energy in accordancewith the positions of the ribs, so as to accurately estimate the wearamount of the aircraft tires per position of each rib.

While the present invention has been described above by reference to theembodiment, it should be understood that the present invention is notintended to be limited to the descriptions and the drawings composingpart of this disclosure. Various alternative embodiments, examples, andtechnical applications will be apparent to those skilled in the artaccording to this disclosure.

For example, the wear amount estimation device 10 has been illustratedwith the case of acquiring the information on the aircraft from theairline 30, but is not limited to this case. The wear amount estimationdevice 10 may acquire the information on the aircraft from any elementother than the aircraft 30.

This application is based upon and claims the benefit of priority fromJapanese Patent Application No. 2017-239708, filed on Dec. 14, 2017, theentire contents of which are incorporated herein by reference.

REFERENCE SIGNS LIST

-   -   10 WEAR AMOUNT ESTIMATION DEVICE    -   11 COMMUNICATION UNIT    -   12 CALCULATION UNIT    -   13 ESTIMATION UNIT    -   20 NETWORK    -   30 AIRLINE    -   40 to 43 AIRCRAFT TIRE    -   50 to 53 RIB    -   60 CIRCUMFERENTIAL GROOVE

1. A wear amount estimation method for estimating a wear amount ofaircraft tires in a state of taxiing indicating a state in which anaircraft runs on a ground under a power of the aircraft, the state oftaxiing including a state of a free rolling run indicating a state inwhich the aircraft runs straight by rolling without braking force actingon the aircraft tires, the method comprising: calculating wear energyE_(P), which depends on an internal pressure of the aircraft tires, inaccordance with the internal pressure and wear energy E_(FR) of theaircraft tires in the state of the free rolling run; calculating wearenergy E_(L), which depends on a load acting on the aircraft tires, inaccordance with the load and the wear energy E_(FR); calculating wearenergy E_(V), which depends on a velocity of the aircraft, in accordancewith the velocity and the wear energy E_(FR); calculating wear energyΔE_(S), which depends on a slip angle caused in the aircraft tires, inaccordance with the slip angle and the wear energy E_(FR); calculatingwear energy ΔE_(B), which depends on a braking force of the aircraft, inaccordance with the braking force and the wear energy E_(FR); andestimating the wear amount wear of the aircraft tires in accordance withthe wear energy E_(P), the wear energy E_(L), the wear energy E_(V), thewear energy ΔE_(S), the wear energy ΔE_(B), and a wear resistance Rindicating a relationship between predetermined wear energy and apredetermined wear amount.
 2. The wear amount estimation methodaccording to claim 1, further comprising: calculating wear energy E_(W)of the aircraft tires generated during a predetermined period of time inaccordance with the wear energy E_(P), the wear energy E_(L), the wearenergy E_(V), the wear energy ΔE_(S), and the wear energy ΔE_(B); andestimating the wear amount wear of the aircraft tires such that the wearenergy E_(W) is divided by the wear resistance R.
 3. The wear amountestimation method according to claim 1, further comprising calculatingthe wear energy E_(P), the wear energy E_(L), the wear energy E_(V), thewear energy ΔE_(S), and the wear energy ΔE_(B) in accordance with aposition of each rib of the respective aircraft tires in a state inwhich the aircraft tires are mounted on the aircraft.
 4. The wear amountestimation method according to claim 3, wherein, when the position ofeach rib of the respective aircraft tires is represented by use of avariable i, the wear energy E_(P) is calculated according to thefollowing formula 1:[Math. 1]E _(P) ^(i)(P)=a _(P) P ² +b _(P) P+c _(P)  (1) where P is the internalpressure, and a_(P), b_(P), and c_(P) are constants, the wear energyE_(L) is calculated according to the following formula 2:[Math. 2]E _(L) ^(i)(L)=a _(L) L ² +b _(L) L+c _(L)  (1) where L is the load, anda_(L), b_(L), and c_(L) are constants, the wear energy E_(V) iscalculated according to the following formula 3:[Math. 3]E _(V) ^(i)(V)=a _(V) V ² +b _(V) V+c _(V)  (3) where V is the velocity,and a_(V), b_(V), and c_(V) are constants, the wear energy ΔE_(S) iscalculated according to the following formula 4:[Math. 4]ΔE _(S) ^(i)(SA)=a _(S)(SA)² +b _(S)(SA)+c _(S) −E _(FR)  (4) where SAis the slip angle, and a_(S), b_(S), and c_(S) are constants, the wearenergy ΔE_(B) is calculated according to the following formula 5:[Math. 5]ΔE _(B) ^(i)(G _(x) ^(BR))=a _(B)(G _(x) ^(BR))² +b _(B)(G _(x) ^(BR))+c_(B) −E _(FR)  (5) where G_(X) ^(BR) is the braking force, and a_(B),b_(B), and c_(B) are constants, the wear energy E_(W) is calculatedaccording to the following formula 6: [Math.  6] $\begin{matrix}{E_{w}^{i} = {\Sigma \; {{E_{P}^{i}(P)} \cdot {E_{L}^{i}(L)} \cdot {E_{V}^{i}(V)} \cdot \left\{ {E_{FR}^{i} + {\Delta \; {E_{S}^{i}(S)}} + {\Delta \; {E_{B}^{i}(B)}}} \right\} \cdot \frac{V\; \Delta \; t}{2\pi \; r}}}} & (6)\end{matrix}$ where Δt is the predetermined period of time, and r is acircling radius of the aircraft, and the wear amount wear^(i) of theaircraft tires is estimated according to the following formula 7:[Math.  7] $\begin{matrix}{{wear}^{i} = \frac{E_{w}^{i}}{R}} & (7)\end{matrix}$ where R is the wear resistance.
 5. The wear amountestimation method according to claim 1, wherein the internal pressureand the velocity are acquired from an airline.
 6. A wear amountestimation device for estimating a wear amount of aircraft tires in astate of taxiing indicating a state in which an aircraft runs on aground under a power of the aircraft, the state of taxiing including astate of a free rolling run indicating a state in which the aircraftruns straight by rolling without braking force acting on the aircrafttires, the device comprising: a calculation unit configured to calculatewear energy E_(P), which depends on an internal pressure of the aircrafttires, in accordance with the internal pressure and wear energy E_(FR)of the aircraft tires in the state of the free rolling run; and anestimation unit configured to estimate the wear mount wear of theaircraft tires, the calculation unit being configured to: calculate wearenergy E_(L), which depends on a load acting on the aircraft tires, inaccordance with the load and the wear energy E_(FR); calculate wearenergy E_(V), which depends on a velocity of the aircraft, in accordancewith the velocity and the wear energy E_(FR); calculate wear energyΔE_(S), which depends on a slip angle caused in the aircraft tires, inaccordance with the slip angle and the wear energy E_(FR); and calculatewear energy ΔE_(B), which depends on a braking force of the aircraft, inaccordance with the braking force and the wear energy E_(FR), theestimation unit being configured to estimate the wear amount wear of theaircraft tires in accordance with the wear energy E_(P), the wear energyE_(L), the wear energy E_(V), the wear energy ΔE_(S), the wear energyΔE_(B), and a wear resistance R indicating a relationship betweenpredetermined wear energy and a predetermined wear amount.
 7. Anon-transitory computer-readable storage medium storing a wear amountestimation program for estimating a wear amount of aircraft tires in astate of taxiing indicating a state in which an aircraft runs on aground under a power of the aircraft, the state of taxiing including astate of a free rolling run indicating a state in which the aircraftruns straight by rolling without braking force acting on the aircrafttires, the program causing a computer of a terminal device to executethe steps of: calculating wear energy E_(P), which depends on aninternal pressure of the aircraft tires, in accordance with the internalpressure and wear energy E_(FR) of the aircraft tires in the state ofthe free rolling run; calculating wear energy E_(L), which depends on aload acting on the aircraft tires, in accordance with the load and thewear energy E_(FR); calculating wear energy E_(V), which depends on avelocity of the aircraft, in accordance with the velocity and the wearenergy E_(FR); calculating wear energy ΔE_(S), which depends on a slipangle caused in the aircraft tires, in accordance with the slip angleand the wear energy E_(FR); calculating wear energy ΔE_(B), whichdepends on a braking force of the aircraft, in accordance with thebraking force and the wear energy E_(FR); and estimating the wear amountwear of the aircraft tires in accordance with the wear energy E_(P), thewear energy E_(L), the wear energy E_(V), the wear energy ΔE_(S), thewear energy ΔE_(B), and a wear resistance R indicating a relationshipbetween predetermined wear energy and a predetermined wear amount.